
228 Ballistics: Theory and Design of Guns and Ammunition
where y
e
is the y-coordinate on the envelope curve. Equation 8.33 can be further rear-
ranged to yield the nal equation of the trajectory envelope:
y
V
g
gx
V
e
e
1
0
2
2
0
2
(8.34)
A typical trajectory envelope is illustrated in Figure 8.2.
To move to a different subject in the study of the vacuum trajectory, when the trajectory of
the projectile is relatively at, certain simplifying assumptions may be made, which allow the
equations of motion to be solved with greater ease. In particular, if we rewrite Equation 8.7 as
yx
gx
=−ta
ec
0
2
2
2
0
(8.35)
we now take its derivative with respect to ϕ
0